1007-4619（2014）01-0061-16Journal of Ｒemote Sensing 遥感学报
Power lines extraction from airborne LiDAＲdata
using spatial domain segmentation
LIU Zhengjun 1，LIANG Jing 1，2，3，ZHANG Jixian 1
1．Chinese Academy of Surveying and Mapping ，Beijing 100830，China ；
2．College Environment and Spatial Informatics ，China University of Mining and Technology ，Xuzhou 221166，China ；
3．Henan Provincial Ｒemote Sensing and Mapping Institute ，Zhengzhou 450003，China Abstract ：Airborne LiDAＲis now becoming a rapid method to acquire three-dimensional coordinates of the ground objects auto-matically ，which has great potential applications on power lines inspection．According to the demand of the intelligent power lines inspection ，a power lines extraction method based on spatial domain segmentation was proposed in this paper．First ，the method a dopted the elevation histogram statistical method to remove ground objects．Second ，pylons along the corridor were identified based on the difference of the point cloud density．Third ，single power lines was isolated from each other based on the distance threshold between two neighborhood lines and height threshold between two neighborhood level of lines using a spatial domain segmentation algorithm．Finally ，a simplified polynomial model was applied to model the geometry of each power line in three-d imensional
space．Experimental results showed that the method can be applied to extract power lines with multiple spans simultaneously ，and demonstrated its potential advantages in power-lines inspection application．
Key words ：power lines extraction ，spatial domain segmentation ，airborne LiDAＲ，elevation histogram ，pylon extraction CLC number ：P207Document code ：A
Citation format ：Liu Z J ，Liang J and Zhang J X．2014．Power lines extraction from airborne LiDAＲdata using spatial domain seg-mentation．Journal of Ｒemote Sensing ，
18（1）：61－76［DOI ：10．11834/jrs．20132231］Ｒeceived ：2012-08-06；Accepted ：2013-08-05；Version of record first published ：2013-08-12
Foundation ：National Key Technology Ｒ＆D Program （No．2012BAB16B01）；China Southern Power Grid Company Limited Program
First author biography ：LIU Zhengjun （1974—），male ，professor ，his research interests are remote sensing of environment ，airborne LiDAＲdata pro-cessing and applications ，and remote sensing change detection from optical imagery and LiDAＲdata．E-mail ：zjliu@casm．ac．cn
1INTＲODUCTION
With the increased power consumption demand from the raid development of economy ，more and more high voltage and long-distance transmission power lines are constructed．Safety i nspection of transmission lines become a large task for the power grid maintenance department．From the 1950's ，the power sector began to use helicopters with digital cameras and infrared photo-graphic apparatus to inspect and maintenance transmission lines．In recent years in some developed countries ，helicopters carried with LiDAＲare used to inspect transmission lines．The airborne LiDAＲsystem can be used to generate Digital Elevation Model （DEM ）and Digital Orthophoto Model （DOM ）describing the three-dimensional topography and geomorphology along the pow-er-lines corridor using the acquired high precision point cloud and aerial digital images．In addition with the accurate three-di-mensional models of power line sags．These data can be used to measure the distances from objects （especially trees ，house ）to wires and distances between individual wires ，d etermining whether the distances between the objects and the power lines meet the safety requirements．
Currently ，studies have been carried out to extract transmis-sion line based on aerial images ，and have achieved certain re-sults．In general ，when extracting power lines from the aerial im-ages ，template algorithms that detect edges presented in images
should be used first ，followed by a Hough transform to extract
pixels of power lines （Zhang ，2006；Li ，2006；Cai ＆Yang ，2009；Wei ，2010）．For power lines extraction using airborne LiDAＲdata ，Melzer and Briese （2004）proposed a method based on t wo-dimensional Hough Transform and estimation of
catenary's parameters to extract transmission lines．McLaughlin （2006）a dopted a supervised knowledge classification method to d iscriminate power lines from the surrounding terrain ，followed by segmenting the point cloud of transmission line into line s egments using local affine model．Clode and Ｒottensteiner （2005）proposed a method to isolate trees from transmission lines points cloud based on evidence theory method．Jwa （2009，2010）proposed a method based on three constraint factors ，i．e．，height from the ground ，direction of transmission line and pylons'location ，and Hough transform to detect transmission lines．Meanwhile ，Vale and Gomes-Mota （2007）presented a
real time scanning line point detection method of transmission line ，which can be used to avoid obstacles when flying at low al-titude．In China ，Ou （2009）and Yu （2011）proposed a trans-mission line extraction method from LiDAＲdata．It first trans-forms three-dimensional points to a two-dimensional space ，and
then uses Hough transform to extract the power lines．Ye （2010）proposed a method that converts point cloud to raster for-mat digital elevation model by height projection and resampling ，and then extracts and fits power lines through line detection in im-
62Journal ofＲemote Sensing遥感学报2014，18（1）
age space．
In summary，the Hough transform is probably the most widely adopted method to extract power lines based on LiDAＲpoints cloud data or aerial images．However，because of the complex and time-consuming calculation procedure，the Hough transform has limitations in practical applications．By analyzing the spatial distribution characteristics of transmission power lines，this paper presents a new automatic extraction method for multi-span power lines extraction based on spatial domain segmen-tation．It separates single power line according to the distance difference of adjacent lines and the elevation difference of adja-cent layer．Ｒesults showed that the method is efficient，and less af-fected by the reduced point cloud density，and robust to missing segment data．
2OVEＲALL PＲOCEDUＲE AND THE PＲE-PＲOCESSING
2．1The basic procedure
First，the power line points should be separated from the numerous original three-dimensional laser point cloud，which is mainly focused on removal of ground points and pylon points．Second，the orientation of the power lines should be determined according to its spatial neighborhood characteristics．Third，each power line points are identified from all the power line point cloud data．Finally，the three-dimensional geometry of power lines is reconstructed．The general flow chart is shown in Fig．1．
Fig．1The flow chart of power line extraction 2．2Ground points removal based on elevation histogram analysis method
The airborne LiDAＲsystem can acquire huge amount of l aser points representing the three-dimensional coordinates of ground，buildings，vegetation，rivers and other earth surface f eatures．These features can interfere with the extraction of trans-mission lines，e．g．，the numerous ground laser points would s ignificantly influence the extracting speed．Therefore，the ground points should be removed firstly before the detection of transmission lines．Elevation histogram analysis method is used in this study to remove the ground points．Meanwhile，since the height of the high voltage wires to ground is normally between 15—50m and the number of ground laser points is much higher than transmission line points，the ground points can be automati-cally removed by considering these two characteristics，and by setting a proper elevation threshold on the elevation histogram．Compared with point cloud filtering methods，this method has another advantage which can remove most tree points and build-ing points simultaneously．If the pylons and transmission lines are located in mountainous terrain area，the histogram analysis method cannot be applied directly．To eliminating the impact of terrain，the normalized Digital Surface Model（nDSM）should be built before applying the method to normalize the laser points of ground object onto a unique height basis（Fig．2）．
To build an nDSM，the original point cloud data was firstly filtered to remove non-ground points by using multi-resolution a-nalysis filtering algorithm（Wang，2008）．Then the Digital Ter-rain Model（DTM）is constructed．After point cloud filtering，the missing ground points in point cloud should be interpolated to fill the holes before constructing nDSM．After evaluating e xisting interpolation methods，we adopted the nearest neighbor interpolation method，since it has a smaller computation load and can produce acceptable hole filling result even in steep terrain a reas．
Note in constructing the nDSM，the one-to-one correspon-dence between the nDSM data and the original data is retained，so that the subsequent extraction of power lines can still be c onducted based on the original data．After the normalization of laser point cloud，the ground points，trees points and house points located on mountainous area will fall on the same height basis，which will significantly facilitate the removal of non-trans-mission line points by selecting an optimal height threshold using the elevation histogram analysis method．
Fig．2The sketch of nDSM
2．3The pylons extraction method based on point cloud density
After the aforementioned steps，the ground points should have been removed．In order to automatically extract power lines among multiple pylons，the exact location of the pylons should be identified．Considering the point density of pylons is relative-
LIU Zhengjun，et al．：Power lines extraction from airborne LiDAＲdata using spatial domain segmentation63
ly larger than both sides of the pylons，we adopted a statistical method by estimating the overall laser point cloud density chan-ges to separate pylons．In order to achieve the accurate point density，it should be calculated along the orientation of transmis-sion line corridor．In detail，all power line points are fitted to straight line segments by estimating the rough direction of power lines using line fitting method．Each power line corridor is then divided into a certain amount of intervals along the corridor d irection in the vertical plane so that the number of points within each interval is counted and the point density is estimated．By determining the extreme values of the laser point density change along the corridor we can identify the exact location of the p ylons．Experiments showed that the method is simple and effec-tive．
3THE POWEＲLINE EXTＲACTION METHOD BASED ON SPATIAL DOMAIN SEGMENTA-TION ALGOＲITHM
3．1The extraction method of power lines
Considering the standard related to transmission line de-sign，when power lines pylons are installed by the electricity sec-tors，any two adjacent layers of transmission lines must have a certain height differences．Similarly，the power lines installed at the same layer also has a certain horizontal distance threshold．Due to this characteristic，the power lines are normally shown as independent distribution point clusters in local space in point cloud．Therefore，using the distance thresholds between different layers of power lines and between the power lines installed at the same layer，it is possible to segment each power lines into differ-ent spatial domain and identify a single power line．Fig．3dem-onstrates the basic idea of segment the power lines into three-d imensional space．
Fig．3The three-dimensional spatial domain segmentation
In addition，the high-voltage transmission lines in space tend to have the following characteristics：some power lines c orresponding to the different layers may distribute in the same vertical plane，while some transmission lines form a pyramid structure，showing that the space between the top lines is small，and the space between the transmission lines located at the lower layers becomes larger，in accompanied with the increased num-ber of power lines．
Considering the above factors，in this study，the power lines data is firstly segmented into several layers in the vertical plane according to its elevation，and then every single line on each layer is separated based on the space difference of adjacent lines．The specific procedure is described as below．
（1）Segmentation of the transmission line point cloud data into multiple single-span transmission line subsets
For a stripe of airborne LiDAＲpoints cloud data，there are often multiple spans of transmission lines．In order to simultane-ously extract multi-span transmission lines and ensure accurate fitting of the transmission line sag，the whole power line corridor data should be segmented into multiple single-span transmission line subsets．
The key to distinguish single span transmission line is the pylons，since a transmission line always span between two py-lons．In section2．2，the pylons'locations were identified based on point cloud density．Therefore，the power line points can be grouped into multiple single span data by determining each point's neighborhood pylons according to its coordinates．（2）Segmentation of transmission lines into multiple layers using histogram analysis method in vertical direction
According to the layered distribution characteristics of transmission line in the vertical direction，the elevation histo-gram of transmission line point cloud also show a typical distribu-tion of multiple peaks interleaved with multiple valleys，as shown in Fig．4．It can be seen that most points are distributed in four intervals，including1—29，115—144，30—53，145—176，while there few points are in other three intervals located at30—53，86—114and145—176，respectively．According to this characteristic，the power lines can be segmented into multiple layers using h istogram analysis method for further processing．
Fig．4Elevation histogram of one-span transmission line
This process includes three steps．First，a number of inter-vals was specified in the vertical plane and the number of points in each elevation interval was calculated and recorded as key-value pairs representing the number of points N
i
and its c
orresponding elevation interval g
x
．Taking into account of the va-rious degrees of sag of the transmission line due to its gravity，the transmission lines were straightened to enhance the distance between the upper and lower layer so that the number of points
on each layer can be counted accurately．Z
bow
represents the val-
ue of power lines sag，and Z
raw
represents the height value of o-
riginal point cloud．Next，we estimated Z
bow
using the X and Y of
the original point data（Eq．（1）），and then subtracted the Z
raw of the original point with Z
bow
again（Eq．（2））to get the height value Z after the power line was straightened．
64Journal ofＲemote Sensing遥感学报2014，18（1）
Z
bow =a（X2+Y2）+b X2+Y
槡2+c（1）
Z=Z
raw
－Z
bow
（2）
where a，b and c are the polynomial parameters of power line's sag in three-dimensional space respectively，and Z is the height value of the straightened power lines．
Finally，the elevation interval where there are no points presented was detected，and the unique dividing line between two adjacent layers was determined．From Fig．4we can see that the dividing line must be in the interval that the number of points is zero．Therefore，the number of points in each elevation inter-val meets the following conditions：
N
i－1
≠0（3）
N
i
=0（4）
where N
i is number of points in the g
i
elevation interval，then
the height range corresponding to g
i
elevation interval may repre-
sent a demarcation zone，and the location of elevation interval g
i is near the lowest sag of power line．Here we adopted Eq．（5）to d etermine the dividing line．
H j
peak =
H
i
+H
i－1
2
（5）
where H j
peak
is the rising edge of the peak valley region of the lay-
er of transmission lines，and H
i
is the height value of the rising
edge of the g
i
elevation interval．For each transmission line point
on the same layer it should meet H j－1
peak
≤h i≤H j peak，where h i is height value of the i th point．If the height value of the laser point falls inside this range，it should belong to the same layer．（3）Identify the single power line in the same layer
In general，multiple transmission lines were distributed in the horizontal direction on the same layer．Therefore，the num-ber of wires on each layer should be judged before single trans-mission line is identified．
Suppose the minimum distance threshold of the transmission
line to the fitting centerline isε
dis
，the point count threshold of a
power line isε
number ，and the total amount of points is N
s
on the
same level．If the following situation is satisfied：
Situation1Suppose dis
i
is the distance from the laser point cloud to the fitted straight line in the XY plane．If the n
umber of points of the same layer that meets dis
i ＜ε
dis
is Num，
and Num≈N
s while Num≥ε
number
，then it indicates that only one
transmission line exists，otherwise multiple transmission lines may exist．
Situation2For multiple power lines，it is necessary to further determine if even number of power lines or odd number of power lines are presented in this layer．
If all points on the same layer are far away from the fitted
line，and all points meet dis
i ＞ε
dis
，then the points on this layer
were divided into two data sets by the fitted lines，which show that there exists at least two transmission lines that is even num-ber of power lines．In this case，with fitted line we can separate the point cloud data into two part of data sets，and repeat the fit-ting process by Situation1and Situation2until all single power lines are separated．The point data of the same layer in step Sit-uation1refers to divided subset data，and N
s
refers to number of sub-data set．
If there exists part of the laser points which is very close to the fitted straight line on the same layer，and the number of these type of points meets the threshold condition of a power line points，it can be reasonably assumed that these points belong to one power line and there are odd number of transmission lines （except one）in the same layer．Therefore，the number of trans-
mission lines could be3，5，7，…，and about2/3N
S
，4/5N
S
，
6/7N
S
，…，points meet dis
i
＞ε
dis
，so selecting2/3N
S
as threshold which points far away from the fitted line，when Num
meets dis
i
＞ε
dis
，the points which meet2/3N
S
＜Num＜N
S
are processed a ccording to the situation of all points on the same layer are far away from the fitted line，and the points which meet
dis
i
＞ε
dis
b elong to the middle power line．
The Situation1and Situation2are iterated until all points are separated into different transmission lines，and complete the extraction of transmission lines in the same layer．Power line points of every layers segmented by Step（2）are further separa-ted using the extraction method applied to the same layer，until all transmission lines are completely extracted．
3．2Modeling of transmission line
To accurately model the geometry of a power line sag，the catenary's equation is usually adopted，which describes the f undamental relationship of wire sag，stress and span．The c ommon form of catenary's equation can be formulated as E q．（6）．
y=
σ0
g
cosh
g（x+C
1
）
σ
()
+C
2
（6）
where cosh is hyperbolic cosine function，C
1
and C
2
is integra-
tion constant which can be determined by the origin of the coor-
dinate system and the initial conditions，x is the span of arc
length，y is the sag of the wire，σ
is the stress of the lowest
wire，g is gravitational acceleration．
Because the calculation process is complicated and its p
arameters are difficult to be calculated，the catenary's equation is
normally expanded as Taylor series to solve the solutions．E
q．（7）is the second-order polynomial equation in two-dimen-
sional space which is expanded from Eq．（6）by Taylor s eries．
Eq．（8）is the expanded polynomial equation in three-d
imensional space．
y=ax2+bx+c（7）
y=kx+b
z=a（x2+y2）+b x2+y
槡2
{
+c
（8）where a and b are the parameters of the polynomial equation，k and b are the projected line parameters in a two-dimensional space．
To obtain the coefficients of the polynomial model，the least
squares method were used．
4EXPEＲIMENT AND ANALYSIS
Two sets of Airborne LiDAＲdata in different areas were se-
lected to verify the validity and reliability of the proposed meth-
od．As shown in Fig．5，Dataset1was acquired by Optech O rion
system in an area where pylons are set up in rugged steep slopes
and surrounded by low trees．The average density of points cloud
is8．21points/m2．Dataset2was gained by Leica ALS70sys-
tem，and the average density of points cloud is13．82points/
m2．The data is in plain areas without violent terrain variation，
LIU Zhengjun，et al．：Power lines extraction from airborne LiDAＲdata using spatial domain segmentation65
and surrounded by tall trees and small buildings．Some trees
higher than the bottom layer of the power lines．The distribution
of Dataset2presents the pyramid，with a single power line loca-
ted at the top layer，two power lines located at the second layer，
six power lines located at the third layer，four power lines loca-
ted at the bottom layer．The algorithm is implemented in C++
programming language．
Fig．5Experiment data
4．1Non-power line point removal and pylons extraction
Fig．6demonstrates the nDSM results produced from the f iltering and interpolation method described in section2．2．From Fig．6，the influence of terrain is well reduced by generation of nDSM．Fig．7shows the results after the ground and most of the trees are removed by using histogram analysis method．The py-lons extraction result is shown in Fig．8．Power line data exclu-ding pylons is shown in Fig．9，in which power line data are f urther optimized and shown as segments for multiple span power lines extraction in the next step．
Fig．6The results of nDSM generation
Fig．7Ｒesult of non-power line removal
Fig．8The pylons extraction results
Fig．9Power line segments after removing the pylons
4．2Extraction of power line
The minimum distance between lowest sag of upper power lines and the highest sag of lower power lines in Dataset2is9．09m while the minimum distance of the same layer is11．73 m．In this experiment，the horizontal distance threshold is set to 2m．32power lines are extracted from the whole data and in0．328s，which means100%rate of extraction．Fig．10（a）shows the e xtracted vectorized power line．Fig．10（b）shows the superimposed effects of power line points cloud and the vector-ized power lines．The minimum distance between lowest sag of upper power lines and the highest sag of lower power lines in Dataset2is6．2m and the minimum distance of the same layer is 2．96m．In this experiment，the horizontal distance threshold is set to2m．28power lines are extracted from the whole data and 1．844s are used to perform the processing，which means100% rate of e xtraction．Fig．10（c）shows the vectorized power line e xtracted，Fig．10（d）shows the superimposed effects of Dataset2 points cloud and the vectorized power lines．
In order to assess the fitting precision of the transmission lines，we used the least squares method to fit a transmission line．Fig．11（a）shows the deviations of all original points Y values and fitting results Y values．Fig．11（b）shows the devia-tions of all o riginal points Z values and fitting results Z values．From the fitting result，the Y deviations are distributed in the range between0．15m and－0．15m，and the mean square error is0．0732m；the Z deviations are distributed in the range between0．04m and－0．04m，and the mean square error is0．0207m，the deviations of individual Z values is up to－0．1 m．The experimental results verified that the polynomial model is applicable to multiple-line fitting，and the deviations of Y values and Z values fully meet the requirements for automatically detec-ting dangerous points and three-dimensional scenes reconstruc-tion．
4．3Test on resampled point cloud with missing s ections and trees influence
In practical power transmission line inspection，due to the influences of flight condition，obstruction，and sensor perform-ance，a section of the transmission line point cloud
with
66Journal ofＲemote Sensing遥感学报2014，18（1）
Fig．10The power lines extraction results of Dataset1and Dataset2
Fig．11The deviation map of Y Values and Z Values
rare or missing points tend to appear occasionally．Therefore，the capability of extracting power line information from such data sets is an important indicator to evaluate the effectiveness of the proposed extraction method．In order to verify missing data effect on the method，Dataset1is resampled to five times of point space and part of the power line section points are removed as shown in Fig．12．The test results on the simulated data set based on Data-set1still has the same extraction results compared with the origi-nal Dataset1．Fig．12shows the effect of power line e xtraction，where A，B，C，D show the locations of the missing data．We can see that even if a larger portion of power line points is miss-ing，the method can still detect and fit the whole transmission lines．
After ground points and the pylons are removed，the remai-ning data points are mainly power lines，with a few residual c anopy and roof points，etc．In order to test the robust of the pow-er line method based on space domain segmentation to the toler-ance of residual crown and other potential corridor barriers，a portion of Dataset1with residual canopy points is used for this experiment．Fig．13shows the results after non-power line point removal，in which residual crowns partly remain．
Fig．12Extraction result from resampled data
Fig．13Dataset after non-power-point removal
Fig．14shows the extraction results directly using space d omain segmentation method．As can be seen，the residual cano-pies have a significant impact on extraction of power line，e．g．，the power lines located at the trees and nearby are not completely extracted，and some crowns are incorrectly fitted as power line segments．
Fig．14Vectorized results of power lines
Since the proposed spatial domain segmentation method in this study is relatively robust to dataset with missing power
line
LIU Zhengjun，et al．：Power lines extraction from airborne LiDAＲdata using spatial domain segmentation67
sections，an elevation threshold segmentation procedure is ap-plied for further removal of the residual crowns．
Fig．15shows the power line extraction results after applying the elevation threshold segmentation．Fig．16shows the effect of overlaying vectorized power line with original point cloud．The experimental result shows that，although the elevation threshold segmentation method may cause some incorrect classifications of power line points into other objects，it does not have significant influences on fitting of the whole power lines．
Fig．15Vectorized result of power lines
Fig．16Overlay of power lines with point clouds 4．4Comparison with existing methods
The TerraSolid software with power line detection module is used for comparison．The basic idea of power line detection with TerraSolid is labeling two points as known points on two adjacent pylons location firstly，and then looking for points belong to the same power line between the two pylons according to the continu-ity of the same power line point cloud．When using TerraSolid to detect power lines，the most critical parameter is the maximum gap，which controls the largest distance of continuous laser point on the same power line．
Compared with TerraSolid software，the extraction method of power line based on space domain segmentation have better re-sults with automatic extraction of power line across multiple py-lons，while TerraSolid software can only extract the transmission lines between two pylons．However，long distance transmission line corridor normally has tens or hundreds of pylons，e xtraction of the transmission lines between neighborhood pylons is usually a labor intensive work with low efficiency．In comparison，the method proposed in the paper can quickly complete the detection of the entire line automatically．
In order to verify the efficiency of spatial domain segmenta-tion method，the proposed method in this paper is compared with the TerraSolid software from time consumption，effectiveness on different point density，and section missing data．The Dataset1 and Dataset2are adopted in this contrast．The results are shown in Table1and Table2．
Table1The comparison of the experimental results using Dataset1
Original dataＲesampled to five times point space Section missing data
Extraction number Time/s
Ｒate of
extraction/%
Extraction
number
Time/s
Ｒate of
extraction/%
Extraction
number
Time/s
Ｒate of
extraction/%
Spatial domain segmentation80．07810080．01610080．078100 TerraSolid8—1008—1008—100
Table2The comparison of the experimental results using Dataset2
Original dataＲesampled to five times point space Section missing data
Extraction number Time/s
Ｒate of
extraction/%
Extraction
number
Time/s
Ｒate of
extraction/%
Extraction
number
Time/s
Ｒate of
extraction/%
Spatial domain segmentation140．18810013．50．09496．43140．172100 TerraSolid14—10013—92．8613—92．86
The experimental results showed that in all three aspects，the extraction method based on spatial domain segmentation had better results compared to the method used in TerraSolid．First，the detection time consumption with TerraSolid cannot be accu-rately estimated since it is a semi-automatic method and thus i nvolved manual work．Second，the extraction rate with TerraSol-id is dependent on the density of point cloud and data quality while the proposed method is more stable．In this study，the ex-traction rate of Dataset2resampled to five times point space is 96．43%by the spatial domain segmentation method，while the extraction rate of TerraSolid is92．86%．For Dataset2with sec-tion missing，the extraction rate of spatial domain segmentation method is100%，while the extraction rate of TerraSolid is92．86%．The demonstration showed that the spatial domain seg-mentation method has a certain advantages over the method used in TerraSolid，both in completeness and time consumption．
5CONCLUSIONS
The paper addresses the independent distribution character-istics of power line point cloud in the local space，and then pres-ents a fast and effective transmission power line extraction meth-od from Airborne LiDAＲdata based on spatial domain s egmentation．The method can not only identify a single transmis-sion power line from unordered point cloud，but also automati-
68Journal ofＲemote Sensing遥感学报2014，18（1）
cally extract transmission lines across multiple pylons．The meth-od is fully automatic accurate，and fast．The experiments show that extracting power line among four pylons takes0．328s，with up to100%of extraction rate．
We adopted an elevation histogram analysis method to r emove ground points．The method is simple and effective，espe-cially for transmission line corridor point cloud data．However，for complex urban environment，the result of the method seems not to be satisfactory，which requires further manual removal of vegetation，building points．Effective filtering method on this ar-ea needs to be studied further．
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刘正军等：空间域分割的机载LiDAＲ数据输电线快速提取69
空间域分割的机载LiDAＲ数据输电线快速提取
刘正军1，梁静
1，2，3
，张继贤11．中国测绘科学研究院，北京100830；
2．中国矿业大学环测学院江苏省资源环境信息工程重点实验室，江苏徐州221116；
3．河南省遥感测绘院，河南郑州450003
摘要：机载LiDAＲ具有快速、直接获取地物3维坐标的能力，在电网高压输电线路安全巡检中具有较大的应用前
景。论文针对机载LiDAＲ输电线智能巡检的需求，提出并实现了一种基于空间域分割的LiDAＲ点云数据输电线自动提取方法。该方法首先利用高程直方图统计法去除地面点，再次利用点云密度差异剔除杆塔，根据相邻线之间的距离差和相邻层的高程差进行单根输电线分离。最后，采用多项式模型在3维空间中重构每根输电线空间坐标。实验结果表明该方法能够快速自动地提取多个杆塔之间的多根输电线数据，具有一定的工程应用价值。关键词：输电线提取，空间域分割，机载LiDAＲ，高程直方图，杆塔提取中图分类号：P207
文献标志码：A
引用格式：刘正军，梁静，张继贤．2014．空间域分割的机载LiDAＲ数据输电线快速提取．遥感学报，
18（1）：61－76Liu Z J ，Liang J and Zhang J X．2014．Power lines extraction from airborne LiDAＲdata using spatial domain seg-mentation．Journal of Ｒemote Sensing ，18（1）：61－76［DOI ：10．11834/jrs．20132231］
收稿日期：2012-08-06；修订日期：2013-08-05；优先数字出版日期：2013-08-12基金项目：国家科技支撑计划项目（编号：2012BAB16B01）；南方电网公司重点科技项目
第一作者简介：刘正军（1974—），男，研究员，主要研究方向为环境遥感、机载激光雷达数据处理与应用、基于光学影像和激光雷达数据的变化检测。E-
mail ：zjliu@casm．ac．cn 1引言
随着中国经济的高速发展，高电压、长距离输电线路越建越多。输电线路安全巡检成为电网维护部门一大任务。从20世纪50年代开始，电力部门开始应用直升飞机搭载数码摄像机、红外摄影仪等仪器对输电线路进行巡检维护。近年来，一些发达国家开始利用直升机搭载激光扫描仪进行线路巡检。机载激光雷达（LiDAＲ）系统可利用获取的高精度点云和航空数码影像快速生成数字高程模型（DEM ）、数字正射影像（DOM ），获得高精度3维线路走廊地形地貌以及走廊地物的精确3维空间信息和导线弧垂3维模型，从而精确、快速地量测线路走廊地物点到导线的距离、导线线间距离等（徐祖舰等，2009），并且判断地物到导线距离是否符合安全距离要求。
目前已有不少学者开展了基于航空影像的输电线提取研究，并取得了一定的成果。一般而言，从航空影像上提取电力线首先利用模板算子进行边缘检测，再利用霍夫变换（Hough ）提取输电线像
素（张吴明等，
2006；李朝阳，2006；蔡克等，2009；韦春桃等，
2010）。在基于机载LiDAＲ数据提取输电线方面，
Melzer 和Briese （2004）提出了一种基于2维Hough 变换和悬链线参数的输电线提取方法；Mclauhlin （2006）提出了一种基于监督知识分类的区分输电线与周边地物的方法，然后利用局部仿射模型将输电线点云分割成段；Clode 和Ｒottensteiner （2005）提出了一种基于证据理论的从输电线点云中分离树木的方法；Jwa 和Sohn （2009，
2010）基于LiDAＲ点云数据利用输电线离地高度、输电线方向、杆塔位置3个约束条件提出了一种输电线提取方法，并利用Hough 变换进行输电线线特征的检测。此外，
Vale 和Gomes-Mota （2007）提出了一种实时扫描线输电线点检测的方法，可用于低空飞行物避障。在国内，欧同庚等人（2009）和余洁（2011）提出了一种基于LiDAＲ数据的输电线提取过程，将3维点云转化到2维空间后，再进行Hough 变换提取输电线。叶岚等人（2010）通过高程投影和重采样将高程分布转换为高程值影像，在影像空间通过直
70Journal ofＲemote Sensing遥感学报2014，18（1）
线检测实现电力线提取和拟合。
综合国内外已有文献，无论是基于航空影像还是基于激光雷达点云数据，大都采用Hough变换提取输电线。然而，由于利用Hough变换在海量激光点云中检测输电线的计算过程复杂，时间消耗大，在实际应用具有一定的局限性。本文在分析输电线空间分布特点的基础上，提出一种基于空间域分割的多档距输电线自动提取方法，该方法根据相邻线之间的距离差和相邻层的高程差对单根输电线进行分离。试验结果表明，该方法计算效率高，受点云密度影响小，对数据缺失也具有较好稳健性，取得了较好的效果。
2总体流程及电力线提取预处理方法
2．1基本流程
从激光雷达数据中提取输电线首先要解决从大量原始激光点云中分离输电线点云的问题，主要是剔除地面点和杆塔，分离出输电线点云。其次，根据输电线的空间特征，判断输电线的走向，从输电线数据点云中识别出每根输电线数据。最后，对输电线数据进行3维重构，恢复输电线的空间几何特性。具体的输电线提取流程如图1所示。
2．2基于高程直方图分析法的地面点剔除
由于机载激光雷达测量系统可以获取大量的激光点云数据，包括地面点、建筑物、植被、河流等地物点，这些背景地物信息往往对输电线的提取造成干扰。尤其是大量的地面激光点云，影响输电线的提取速度。因此，检测输电线之前，首先要进行地面点去除。本文采用高程直方图分析法去除地面点。由于高压线的架空距离一般在离地15—5 0m，且获得的地面激光点数量远远高于输电线的点云数量。利用这些特点，可通过高程直方图设置合适的高程阈值，自动剔除地面点。采用这种方法剔除地面点还有另外一个优点，可以一次性剔除大部分的树木与房屋；而若采用点云滤波方法，还需对树木和房屋进一步分类剔除。对于杆塔架设在地势起伏的山区，为消除地形影响，在应用该方法之前还要构建归一化数字表面模型（nDSM）使激光点归一化在同一水平面再进行处理（图2）。
图1输电线提取流程图
图2归一化表面模型（nDSM）示意图
nDSM生成过程首先要对原始点云数据进行滤波，剔除非地面点云，得到数字地形模型（DTM）。本文采用多分辨率分析滤波算法（王刃，2008）对数据进行滤波。点云滤波完成之后，需要对地面点上空缺的位置进行内插，补上相应点云，以便进行nDSM构建。经对比分析已有内插方法，论文采用最近邻插值法对点云数据进行内插。最近邻插值法计算量小，能较好地弥补地形剧烈变换的不足。
本文在构建nDSM过程中保留了nDSM结果与原始数据的一一对应关系，后续的电力线提取等操作仍然在剔除地面点的原始数据上进行。在进行激光点云归一化处理后，位于高处的地面点、树木、房屋点云将落在同一平面，可以更方便地利用高程直方图分析法剔除非电力线点云
。
刘正军等：空间域分割的机载LiDAＲ数据输电线快速提取71
2．3基于密度的杆塔提取方法
经过上述步骤处理后，地面点已被剔除。为实现多个杆塔间输电线的自动提取，需进行杆塔的剔除。为此，需要找出杆塔的准确位置。利用杆塔的点云密度比较大，相邻的两边点云密度相对变小的特点，本文采用整体激光点云密度统计法分离杆塔。为了准确统计杆塔的点云密度，需要在输电线走向上对其进行统计。本文将所有点云数据进行直线拟合，判断电力线的大致走向，然后在电力线走向所在的垂直平面内，沿其方向划分为N个间隔，统计每个间隔内点云的数量。通过判断激光脚点密度变化的极值点得到杆塔所在位置。实验证明该方法简单有效。
3基于空间域分割的输电线提取
3．1输电线提取方法
按照输电线路设计的相关标准规范，电力部门在进行输电线布设时，上下层分布的两层输电线间必须具有一定的高差要求；同样，在同一层上分布的输电线间水平方向上也具有一定的间隔宽度。根据这一特点，输电线在激光点云数据的局部空间范围内呈现独立分布，因此可以利用空间中的线间距差分离每根输电线，即在空间域内分割输电线（图3）。
图33维空间分割
此外，高压输电线在空间中还往往具有以下特点：有些上下层相对应的输电线分布在同一个垂面内，而有些输电线分布结构呈现金字塔形式，即顶层输电线线间距小，下面一层输电线线间距变大或输电线条数增加。
综合考虑上述因素，本文在进行空间域分割输电线的过程中，先在垂直面内按高程将输电线数据分割成多个输电线层面，然后在每一个层面内根据相邻线间距差进行分离单根输电线。具体实现方法如下：
（1）将输电线走廊点云数据分割成多个单档距输电线点云子集
对于一个条带的机载LiDAＲ点云数据，往往包含多个档距输电线，为实现多档距的输电线同时提取，并保证准确拟合导线弧垂，需要将整个输电线走廊数据划分成多个单档距的输电线点云子集。
区分单个档距输电线的标志是中间分布的杆塔，两个杆塔之间跨越的输电线即是一个档距。在本文2．2节中已经根据密度分割出杆塔，因此，可以通过判定与输电线点最邻近的两个杆塔，将输电线数据划分成多个单挡距数据。
（2）利用直方图统计分析法在高程方向对输电线进行分层
根据输电线在高程方向上分层的特点，其形成的点云数据在高程直方图分布也具有多峰多谷的形态特点（图4）。从图4中可看出，点云密集分布在1—29、54—85、115—144、177—200等4个区间内，而在30—53、86—114、145—176等3个区间段内点云数量为0。根据这一特性，可利用直方图统计分析法将输电线分成多个层以便进一步处理。
图4单档距输电线高程分布直方图
这个过程分为3个步骤：首先在垂直平面内，划分出多个间隔，统计每个高程间隔内的点云数量，记录下点云数量N i和各个高程间隔序号g x。考虑到输电线路因受重力影像造成不同程度的下垂，为了更好地统计出每层的点云数量，在统计高程间隔内的点云数量之前，先对输电线进行拉直处理，增大上下层之间的间距。再次本文利用原始每个点云数据的X和Y值按式（1）得到一个Z bow，再
72Journal ofＲemote Sensing遥感学报2014，18（1）
用原始点的Z raw减去Z bow（式（2）所示），即可计算
出拉直后的输电线点云的高程值Z。
Z
bow =a（X2+Y2）+b X2+Y
槡2+c（1）
Z=Z
raw
－Z
bow
（2）
式中，a、b、c是3维空间中电力线弧垂多项式参数，Z
bow
是求得的电力线弧垂值，Z raw是原始的点云高程值，Z是电力线拉伸后的点云高程值。
最后，判断高程间隔内点云数量为0的区域，并确定唯一一个相邻两层间的分界线。由图4可以看出分界线必定在点数为0的区域内，因此若高程间隔内的点云数量满足如下条件：
N
i－1
≠0（3）
N
i
=0（4）式中，N i是第g i个高程间隔内的点数量，则第g i个高程间隔对应的高程范围是一个分界区域，高程间隔g i所在的位置在输电线的最低弧垂附近，论文采用式（5）确定高程分界线。
H j
peak =
H
i
+H
i－1
2
（5）
式中，H j peak是第j层输电线的峰谷上沿值，H i是第g i 个高程间隔的上沿高程值。同一层输电线上的点云满足H j－1peak≤h i≤H j peak（h i表示第i个激光点的高程），若激光点的高程值在此范围之内，则属于同一层输电线。
（3）同层输电线中识别单根输电线
常规情况下，在水平方向上的同一层上分布多根输电线，所以在识别单根输电线之前，需判断每一层输电线上有几根导线。
设输电线到拟合中心线的最小距离阈值为εdis，一根输电线上点云数量阈值为εnumber，假设同一层上总点云数量为N s，若有如下情况：
情况1设dis
i
是激光点云在XY平面上到拟合直线的距离。若同一层上满足dis i＜εdis的点云数量为Num，有Num≈N s，且Num≥εnumber，则说明该层只有一根输电线，否则存在多根输电线。
情况2对存在多根输电线的情况，必须进一步判断该层有偶数根输电线还是奇数根输电线。
如果同一层上的所有点云离拟合直线比较远，满足所有点云的dis i＞εdis，则说明该层上的点云被拟合直线分成两部分子数据集，存在至少两根输电线，即该层有偶数根输电线。此时，以拟合的中心线为界将数据划分为两部分数据集，然后在划分的两部分输电线数据集里，再分别按情况1、情况2进行分线，直到分离出所有单根输电线，此时情况1中的同一层数据指在该步中分成两部分后的子数据集，相应的N s也指子数据集中点的数量。
如果同一层上的激光点云中有部分点云离拟合直线很近，并且这些点的数量满足一根输电线的点云数量阈值条件，说明这部分点云位于拟合的中心线附近，则该层有奇数根输电线（除去一根的情况）。由此可知该层输电线数量可能为3、5、7、…，有约2/3N s、4/5N s、6/7N s、…，的点云满足dis i＞εdis，因此以2/3N s为离拟合直线比较远的点云的数量阈值，当满足dis i＞εdis的点云数量为Num，满足2/3N
s
＜Num＜N
s
条件的点云按点云离拟令直线较远情况处理进行处理，满足dis i＜εdis的点云为中间的一根输电线数据。
经过情况1两个步骤的循环迭代，直到将所有点云划分到不同的输电线中，即完成了同层输电线的提取。利用同层输电线的提取方法对步骤（2）中分离出的每层数据进行处理，即可完成所有输电线的提取。
3．2输电线建模
输电线路安全检测时，为方便量测输电线路周围地物到导线的距离以及确定危险地物位置，判断是否在安全范围之内，需要获得准确的导线弧垂坐标。一般采用悬链方程对导线弧垂进行空间建模，它描述了导线弧垂与应力、比载及档距之间的基本关系。悬链方程的普通形式为
y=
σ0
g
cosh
g（x+C
1
）
σ
()
+C
2
（6）式中，cosh是双曲余弦函数，C1和C2为积分常数，其值可根据坐标原点的位置及初始条件而定。x表示弧长档距，y表示导线的弧垂，σ0为导线最低点的应力，g为重力加速度。
由于悬链线方程的普通形式计算较为复杂，参数不易求解，可将其按照泰勒级数进行展开。式（7）是式（6）经泰勒级数展开后在2维空间中表示的二次多项式方程，式（8）是转化到3维空间中的多项式方程。
y=ax2+bx+c（7）y=kx+b
z=a（x2+y2）+b x2+y
槡2
{
+c
（8）式中，a、b是多项式方程参数，k、b是输电线在2维平面上的投影直线参数。
为了获得多项式模型系数，本文采用最小二乘方法进行拟合求解。
刘正军等：空间域分割的机载LiDAＲ数据输电线快速提取73
4实验结果及分析
为了验证本文提出方法的有效性和可靠性，选取不同地区两组机载LiDAＲ数据进行试验验证。如图5所示，数据1是采用Optech Orion系统获取的某地区点云数据，杆塔架在凹凸不平的陡坡处，周围有低矮的树木，平均点云密度8．21个/m2。数据2是徕卡ALS70系统获取的某地区数据，点云密度为13．82个/m2，该数据是在平原地区，地形没有大的起伏变化，周围有高大的树木和低矮的平房，而且有些树木高度已经超过最底层输电线。数据2的电力线分布呈现金字塔型，顶层分布一根电力线，第2层是两根电力线，第3层是6根电力线，最底层是4根电力线。算法采用C++语言编程实现。
图5实验数据
4．1非电力线剔除及杆塔提取实验
图6是利用上文提到的滤波方法和插值法构建的nDSM结果，从图中可以看出，经过nDSM后很好地消除了地形的影响。图7是利用直方图分析法剔除地面点和大部分树木的结果。图8是杆塔提取结果，图9是剔除杆塔后的电力线数据，电力线数据得到进一步优化，有利于下一步多档距间电力线快速提取。
4．2输电线提取实验
经量测数据1的上层输电线数据弧垂最低点到下层输电线最高点的最小距离是9．09m，同层输电线间的最小间距是11．73m，实验中水平距离阈值设置为2m。整个数据共提取32根输电线，耗时0．328s，提取率为100%。图10（a）是数据1提取的矢量线效果图，图10（b）数据1输电线点云和矢量线叠加的效果图。数据2中上层输电线数据弧垂最低点到下层输电线最高点的最小距离是6．2 m，同层输电线间的最小间距是2．96m，实验中，水平距离阈值设置为2m。整个数据共提取28根输电线，耗时1．844s，提取率为100%。图10（c）是数据2提取的矢量线效果图，图10（d）是数据2输电线点云和矢量线叠加的效果图。
图6nDSM构建结果
图7非电力线剔除结果
图8杆塔提取结果
图9剔除杆塔后电力线数据
为了评估本文提出的多项式模型拟合输电线的精度，本文利用最小二乘方法对数据1中一根输电线进行拟合。图11（a）和图11（b）分别是所有原始点云的Y值和Z值与拟合结果的Y值和Z值偏差图
。
74Journal ofＲemote Sensing遥感学报2014，18（1）
图10数据1、数据2矢量线与点云叠加效果
图11Y值、Z值偏差值分布图
从拟合结果可知，Y值偏差在0．15—－0．15区间内波动，偏差中误差为0．0732；Z值偏差主要在0．04—－0．04区间内波动，偏差中误差为0．0207，个别点的Z值偏差达到－0．1。该实验结果验证了多项式模型应用于多根电力线拟合的可适用性，Y值和Z值偏差精度对于危险点自动检测和3维场景构建来说，都完全满足要求。
4．3数据抽稀和缺失及树木影响实验
在实际输电线巡检中，由于飞行条件、障碍物、传感器性能等因素影响，往往会出现某段输电线点云数据稀少或缺失的情况，输电线提取方法能否正确提取该段输电线将是评价该方法好坏的一个指标。为了验证本方法对缺失数据的影响，本文将数据1抽稀和删除部分点云进行验证。经试验发现，对数据1抽稀5倍后仍得到同样的提取结果。图12是对缺失数据提取的效果，图12中A、B、C、D 箭头指向处是缺失数据位置，可以看出即使点云数据有较大部分缺失，但是仍可以检测出缺失数据输电线并拟合成完整的输电线。
图12缺失数据1提取输电线效果
经过地面点和杆塔剔除后，剩下数据主要为电力线点云，但部分数据中还残存一些树冠、屋顶等。为了测试基于空间域分割方法对残存的树冠等潜在障碍物的容忍度，本文截取数据1中3个档距的点云数据进行试验。图13是原始数据经过非电力线剔除后的结果，可以看出，该数据中仍然残存一部分树冠。
图13剔除非电力线点云后的电力线数据
图14是直接对该数据利用基于空间域分割法进行电力线提取的效果，从图中可以看出，残存的树冠对电力线提取有较大影响，树木所在位置相对应的电力线没有全部提取出来，同时树冠被当做电
刘正军等：空间域分割的机载LiDAＲ数据输电线快速提取75
力线拟合成线段。
由于本文提出的基于空间域分割法对电力线点
云数据缺失的情况容忍度较高，所以对该数据再次利
用高程阈值进行数据分割，进一步剔除残存树冠。
图14电力线矢量化结果
图15是进行二次分割去除残存树冠后，提取的电力线，图16是矢量化的电力线与点云叠加的效果。实验结果表明，二次分割后，虽然对电力线数据造成部分的缺失，但是对整根电力线的拟合不会产生影响。
图15提取的电力线矢量化效果
4．4与现有方法的对比分析
采用TerraSolid软件电力线检测模块与本文算
图16电力线与点云叠加效果
法进行比较。TerraSolid检测电力线的基本步骤是先在两个相邻电塔的位置上标出两个点作为已知点，根据同一根电力线上点云的连续性，在这两个电塔间寻找属于同一根电力线上的点云。TerraSolid 检测电力线最关键的参数是Max gap，控制同一根电力线上连续激光点的最大间距。
与TerraSolid软件相比，基于空间域分割的输电线提取方法具有同时自动提取多个杆塔间输电线的优越性，而TerraSolid软件每次只能提取两个杆塔间的输电线。在长距离跨越的输电线走廊中，杆塔个数达几十个，若每次只提取两塔间输电线，过程比较繁琐，总的检测效率并不高，而利用本文提取输电线的方法可快速自动地完成整个线路的检测。
为了验证基于空间域分割法提取输电线的效率，本文分别用数据1和数据2一个档距的输电线数据从提取时间、点云密度、数据缺失多个角度与TerraSolid软件检测效果进行比较分析，比较结果见表1和表2。
表1数据1试验结果对比
原始数据抽稀5倍缺失数据
提取条数提取时间/s提取率/%提取条数提取时间/s提取率/%提取条数提取时间/s提取率/%基于空间域分割法80．07810080．01610080．078100 Terrasold检测8—1008—1008—100
表2数据2试验结果对比
原始数据抽稀5倍缺失数据
提取条数提取时间/s提取率/%提取条数提取时间/s提取率/%提取条数提取时间/s提取率/%基于空间域分割法140．18810013．50．09496．43140．172100 Terrasold检测14—10013—92．8613—92．86
由试验结果可知，无论是从提取时间、点云密度还是数据缺失影响方面，基于空间域分割的输电线提取方法都取得了比较好的效果。TerraSold检测电力线由于其时间无法精确估计，单从提取率来看，它的提取率也很高，但是对于形态分布特殊的电力线，
其点云密度大小和数据缺失情况对提取结
76Journal ofＲemote Sensing遥感学报2014，18（1）
果具有一定影响。数据2抽稀5倍后基于空间域分割法提取率为96．43%，Terrasolid软件提取率为9 2．86%。对于数据2缺失数据情况基于空间域分割法提取率为100%，Terrasolid软件提取率为9 2．86%。基于空间域分割法提取电力线具有一定的优越性，而且提取时间非常快。
5结论
本文在分析输电线在局部空间范围内独立分布的特点上，提出了一种基于空间域分割的机载L iDAＲ数据输电线快速提取方法，可有效地从激光点云数据中提取输电线。该方法不仅可以识别单根输电线，而且实现了多个杆塔间输电线自动提取，具有自动化水平高、速度快的特点。试验表明，4个杆塔间输电线提取仅仅需要0．328s，输电线提取率可达100%。
本文采用高程直方图分析法剔除地面点，算法简单高效，尤其对于条带输电线路数据剔除地面点效果非常好，但是对于复杂的城区环境数据该方法分离输电线数据不太理想，还需进一步手工去除植被、建筑物点云，其方法有待进一步研究。
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